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Public data repositories have enabled researchers to compare results acrossmultiple genomic studies in order to replicate findings. A common approach isto first rank genes according to an hypothesis of interest within each study.Then, lists of the top-ranked genes within each study are compared acrossstudies. Genes recaptured as highly ranked (usually above some threshold) inmultiple studies are considered to be significant. However, this comparisonstrategy often remains informal, in that type I error and false discovery rate(FDR) are usually uncontrolled. In this paper, we formalize an inferentialstrategy for this kind of list-intersection discovery test. We show how tocompute a $p$-value associated with a "recaptured" set of genes, using aclosed-form Poisson approximation to the distribution of the size of therecaptured set. We investigate operating characteristics of the test as afunction of the total number of studies considered, the rank threshold withineach study, and the number of studies within which a gene must be recaptured tobe declared significant. We investigate the trade off between FDR control andexpected sensitivity (the expected proportion of true-positive genes identifiedas significant). We give practical guidance on how to design a bioinformaticlist-intersection study with maximal expected sensitivity and prespecifiedcontrol of type I error (at the set level) and false discovery rate (at thegene level). We show how optimal choice of parameters may depend on particularalternative hypothesis which might hold. We illustrate our methods usingprostate cancer gene-expression datasets from the curated Oncomine database,and discuss the effects of dependence between genes on the test.

Statistical tests for the intersection of independent lists of genes: Sensitivity, FDR, and type I error control